Solved Exercises on Hundreds, Tens and Ones Subtraction in Grade 2

Master place value subtraction: hundreds, tens and ones with borrowing and regrouping through these 10 detailed exercises with visual representations and step-by-step solutions.

Solution: Exercises 1 to 5
1 Simple subtraction
Exercise 1
Subtract: 347 - 123
Definition:

Place value subtraction: Subtracting numbers by working with hundreds, tens, and ones separately, starting from the ones place.

Subtraction method:
  1. Line up numbers by place value
  2. Subtract ones first, then tens, then hundreds
  3. No borrowing needed when top digit ≥ bottom digit in each place
HUNDREDS
3 - 1 = 2
TENS
4 - 2 = 2
ONES
7 - 3 = 4
Step 1: Align numbers by place value

347

- 123

-----

Step 2: Subtract ones place

7 - 3 = 4

Step 3: Subtract tens place

4 - 2 = 2

Step 4: Subtract hundreds place

3 - 1 = 2

347 - 123 = 224
Final answer:

347 - 123 = 224

Applied rules:

• Place value alignment: Match digits by position

• Right-to-left subtraction: Start with ones, then tens, then hundreds

• No borrowing needed: When top digit ≥ bottom digit in each place

2 Borrowing from tens
Exercise 2
Subtract: 253 - 127
Definition:

Borrowing: Taking 1 from a higher place value when the top digit is smaller than the bottom digit.

Borrowing situation:

Ones: 3 < 7 → Need to borrow from tens place

BEFORE
253
→
AFTER BORROWING
24[13]
HUNDREDS
2 - 1 = 1
TENS
4 - 2 = 2
ONES
13 - 7 = 6
Step 1: Check ones place

3 < 7, so we need to borrow from tens

Step 2: Borrow from tens place

Take 1 ten from 5 tens: 5 - 1 = 4 tens

Add 10 ones to 3 ones: 3 + 10 = 13 ones

Step 3: Subtract ones place

13 - 7 = 6

Step 4: Subtract tens place

4 - 2 = 2

Step 5: Subtract hundreds place

2 - 1 = 1

253 - 127 = 126
Final answer:

253 - 127 = 126

Applied rules:

• Borrowing rule: When top digit < bottom digit, borrow 1 from next higher place

• Regrouping: 1 ten = 10 ones, 1 hundred = 10 tens

• Adjustment: Reduce borrowed place by 1, increase receiving place by 10

3 Borrowing from hundreds
Exercise 3
Subtract: 405 - 178
Definition:

Multiple borrowing: When multiple place values require borrowing due to insufficient values.

Borrowing situations:

Ones: 5 < 8 → Need to borrow from tens

Tens: 0 < 7 → Need to borrow from hundreds first

START
405
→
BORROW FROM HUNDREDS
3[10]5
→
BORROW FROM TENS
3[9][15]
HUNDREDS
3 - 1 = 2
TENS
9 - 7 = 2
ONES
15 - 8 = 7
Step 1: Check ones place

5 < 8, so we need to borrow from tens

Step 2: Check tens place

0 < 7, so we need to borrow from hundreds first

Step 3: Borrow from hundreds

Take 1 hundred from 4 hundreds: 4 - 1 = 3 hundreds

Add 10 tens to 0 tens: 0 + 10 = 10 tens

Step 4: Now borrow from tens

Take 1 ten from 10 tens: 10 - 1 = 9 tens

Add 10 ones to 5 ones: 5 + 10 = 15 ones

Step 5: Subtract each place

Hundreds: 3 - 1 = 2

Tens: 9 - 7 = 2

Ones: 15 - 8 = 7

405 - 178 = 227
Final answer:

405 - 178 = 227

Applied rules:

• Chain borrowing: When lower place needs borrowing but higher place has 0

• Sequential borrowing: Borrow from higher place first, then work down

• Multiple adjustments: Each borrowing affects the place values accordingly

Solution: Exercises 6 to 10
4 Subtraction with zeros
Exercise 4
Subtract: 500 - 237
Definition:

Subtraction with zeros: When the minuend has zeros in tens or ones place, borrowing requires special attention.

Borrowing situation:

Ones: 0 < 7 → Need to borrow from tens

Tens: 0 < 3 → Need to borrow from hundreds

START
500
→
BORROW FROM HUNDREDS
4[10]0
→
BORROW FROM TENS
4[9][10]
HUNDREDS
4 - 2 = 2
TENS
9 - 3 = 6
ONES
10 - 7 = 3
Step 1: Check ones place

0 < 7, need to borrow from tens

Step 2: Check tens place

0 < 3, need to borrow from hundreds first

Step 3: Borrow from hundreds

5 hundreds → 4 hundreds, 0 tens → 10 tens

Step 4: Borrow from tens

10 tens → 9 tens, 0 ones → 10 ones

Step 5: Subtract each place

4 - 2 = 2 hundreds

9 - 3 = 6 tens

10 - 7 = 3 ones

500 - 237 = 263
Final answer:

500 - 237 = 263

Applied rules:

• Zero handling: Zeros require borrowing from higher place values

• Sequential borrowing: Work from highest place down when multiple borrows needed

• Regrouping: Maintain place value structure after borrowing

5 Comparing subtraction results
Exercise 5
Which is greater: 623 - 287 or 514 - 196?
Definition:

Comparison after subtraction: Calculating both differences and comparing the results.

623 - 287
623 → 5[11][13], 5-2=3, 11-8=3, 13-7=6
514 - 196
514 → 4[10][14], 4-1=3, 10-9=1, 14-6=8
Step 1: Calculate 623 - 287

Ones: 3 < 7 → Borrow: 13 - 7 = 6

Tens: 1 < 8 (after borrowing) → Borrow: 11 - 8 = 3

Hundreds: 5 - 2 = 3

Result: 336

Step 2: Calculate 514 - 196

Ones: 4 < 6 → Borrow: 14 - 6 = 8

Tens: 0 < 9 (after borrowing) → Borrow: 10 - 9 = 1

Hundreds: 4 - 1 = 3

Result: 318

Step 3: Compare results

336 > 318

623 - 287 = 336, 514 - 196 = 318
Final answer:

623 - 287 = 336 is greater than 514 - 196 = 318

Applied rules:

• Separate calculations: Solve each subtraction independently

• Comparison: Compare final results using place value

• Verification: Check each subtraction for accuracy

6 Word problem subtraction
Exercise 6
Sarah had 425 stickers. She gave 189 stickers to her friend. How many stickers does she have left?
Definition:

Word problem subtraction: Identifying minuend and subtrahend from context and solving using place value subtraction.

Problem setup:

Minuend: 425 (total stickers)

Subtrahend: 189 (stickers given away)

START
425
→
BORROWING NEEDED
3[11][15]
HUNDREDS
3 - 1 = 2
TENS
11 - 8 = 3
ONES
15 - 9 = 6
Step 1: Identify the operation

"How many left" indicates subtraction: 425 - 189

Step 2: Check ones place

5 < 9 → Need to borrow from tens

Step 3: Check tens place

1 < 8 (after borrowing) → Need to borrow from hundreds

Step 4: Borrow from hundreds

4 hundreds → 3 hundreds, 2 tens → 12 tens

Step 5: Borrow from tens

12 tens → 11 tens, 5 ones → 15 ones

Step 6: Subtract each place

3 - 1 = 2 hundreds

11 - 8 = 3 tens

15 - 9 = 6 ones

425 - 189 = 236
Final answer:

Sarah has 236 stickers left.

Applied rules:

• Word problem identification: Determine minuend and subtrahend

• Contextual meaning: Connect mathematical result to real-world situation

• Multi-step borrowing: Handle sequential borrowing when needed

7 Verification by addition
Exercise 7
Verify: 563 - 247 = 316 by adding back.
Definition:

Subtraction verification: Adding the difference to the subtrahend should equal the minuend.

SUBTRACTION
563 - 247 = 316
VERIFICATION
316 + 247 = 563
Step 1: Perform the subtraction

563 - 247 = 316

(Ones: 3 < 7 → Borrow: 13-7=6, Tens: 5-4=1, Hundreds: 5-2=3)

Step 2: Add difference to subtrahend

316 + 247

Ones: 6 + 7 = 13 → Write 3, carry 1

Tens: 1 + 4 + 1 = 6

Hundreds: 3 + 2 = 5

Result: 563 ✓

Step 3: Verify the result

Since 316 + 247 = 563, our subtraction was correct

563 - 247 = 316, 316 + 247 = 563
Final answer:

The subtraction 563 - 247 = 316 is correct.

Applied rules:

• Verification method: Difference + Subtrahend = Minuend

• Reverse operation: Addition undoes subtraction

• Accuracy check: Always verify important calculations

8 Mixed operations
Exercise 8
Calculate: 456 - 123 + 78
Definition:

Mixed operations: Performing subtraction and addition from left to right following order of operations.

FIRST: 456 - 123
456 → 333
THEN: 333 + 78
333 → 411
Step 1: Perform subtraction first

456 - 123

Ones: 6 - 3 = 3

Tens: 5 - 2 = 3

Hundreds: 4 - 1 = 3

Result: 333

Step 2: Perform addition next

333 + 78

Ones: 3 + 8 = 11 → Write 1, carry 1

Tens: 3 + 7 + 1 = 11 → Write 1, carry 1

Hundreds: 3 + 0 + 1 = 4

Result: 411

Step 3: Final result

456 - 123 + 78 = 411

(456 - 123) + 78 = 333 + 78 = 411
Final answer:

456 - 123 + 78 = 411

Applied rules:

• Order of operations: Left to right for same precedence operations

• Sequential calculation: Complete one operation before moving to next

• Carry/borrow handling: Apply place value rules for each operation

9 Missing number problems
Exercise 9
What number subtracted from 634 gives 287?
Definition:

Missing number problems: Using inverse operations to find unknown values in subtraction equations.

Problem setup:

634 - ? = 287

This means ? = 634 - 287

SETUP
634 - 287
→
BORROWING NEEDED
5[12][14]
HUNDREDS
5 - 2 = 3
TENS
12 - 8 = 4
ONES
14 - 7 = 7
Step 1: Set up the equation

634 - ? = 287

To find ?, subtract 287 from 634: 634 - 287

Step 2: Check ones place

4 < 7 → Need to borrow from tens

Step 3: Check tens place

2 < 8 (after borrowing) → Need to borrow from hundreds

Step 4: Borrow from hundreds

6 hundreds → 5 hundreds, 3 tens → 13 tens

Step 5: Borrow from tens

13 tens → 12 tens, 4 ones → 14 ones

Step 6: Subtract each place

5 - 2 = 3 hundreds

12 - 8 = 4 tens

14 - 7 = 7 ones

634 - 287 = 347
Final answer:

The number is 347.

Applied rules:

• Inverse operations: To find subtrahend, subtract difference from minuend

• Equation setup: Translate word problem to mathematical equation

• Verification: Check: 634 - 347 = 287

10 Pattern recognition
Exercise 10
Continue the pattern: 500, 450, 400, 350, __, __
Definition:

Number patterns: Identifying the rule by finding the difference between consecutive numbers.

500 - 450
50
450 - 400
50
400 - 350
50
Step 1: Find the pattern

500 - 450 = 50

450 - 400 = 50

400 - 350 = 50

The pattern is subtracting 50 each time

Step 2: Continue the pattern

350 - 50 = 300

300 - 50 = 250

Step 3: Verify the pattern

Each subtraction follows the same rule: subtract 50

500, 450, 400, 350, 300, 250
Final answer:

The next two numbers are 300 and 250.

Applied rules:

• Pattern recognition: Find the difference between consecutive terms

• Consistent subtraction: Apply the same operation repeatedly

• Verification: Check that the pattern continues consistently

Place Value Subtraction Rules and Methods
Minuend - Subtrahend = Difference
Subtraction Formula
ONES PLACE
1
Rightmost position
Subtract first
TENS PLACE
10
Second from right
Subtract second
HUNDREDS PLACE
100
Third from right
Subtract third
Key definitions:

Minuend: The number being subtracted from

Subtrahend: The number being subtracted

Difference: The result of subtraction

Borrowing: Taking 1 from a higher place value when needed

Regrouping: Changing the form of a number for easier calculation

Subtraction methodology:
  1. Align numbers: Match digits by place value
  2. Check each place: See if top digit ≥ bottom digit
  3. Borrow if needed: When top digit < bottom digit
  4. Subtract systematically: Right to left (ones, tens, hundreds)
Tip 1: Always start from the ones place and move left.
Tip 2: Borrow when top digit is smaller than bottom digit.
Tip 3: When borrowing: reduce the higher place by 1, add 10 to the lower place.
Tip 4: Verify your answer by adding the difference to the subtrahend.
Common errors: Forgetting to borrow, incorrect regrouping, misaligning digits, subtracting bottom from top instead of top from bottom.
Learning tips: Practice with visual aids like base ten blocks, use place value charts, verify answers by addition.
Place value subtraction rules:

• Alignment rule: Match digits by place value columns

• Borrowing rule: When top digit < bottom digit, borrow 1 from next higher place

• Regrouping rule: 1 hundred = 10 tens, 1 ten = 10 ones

• Direction rule: Subtract from right to left (ones, tens, hundreds)

• Verification rule: Difference + Subtrahend = Minuend

Detailed Summary: Hundreds, Tens and Ones Subtraction
Key Concepts and Definitions:

Place value subtraction: A method of subtracting numbers by working with hundreds, tens, and ones separately, starting from the ones place and moving to the left.

Borrowing: Taking 1 from a higher place value when the digit in the current place is smaller than the digit being subtracted.

Regrouping: Changing the form of a number by exchanging between place values (e.g., 1 ten = 10 ones).

Minuend: The number from which another number is subtracted.

Subtrahend: The number that is subtracted.

Difference: The result of the subtraction.

Core Rules and Laws:

• Place value alignment: Numbers must be aligned by their place values (ones under ones, tens under tens, etc.)

• Borrowing law: When the top digit is less than the bottom digit, borrow 1 from the next higher place value

• Exchange law: 1 hundred = 10 tens, 1 ten = 10 ones

• Subtraction direction: Always subtract from right to left (ones, tens, hundreds)

• Inverse verification: Difference + Subtrahend = Minuend

Step-by-Step Method:
  1. Align the numbers: Write the numbers vertically with place values lined up
  2. Start from ones: Begin subtraction with the ones place
  3. Check each place: If top digit ≥ bottom digit, subtract directly
  4. Borrow when needed: If top digit < bottom digit, borrow 1 from the next higher place
  5. Continue to tens: Move to tens place and repeat the process
  6. Continue to hundreds: Move to hundreds place and repeat the process
  7. Write the difference: Combine all results from each place value
  8. Verify: Add the difference to the subtrahend to ensure it equals the minuend
Examples:

Simple subtraction: 456 - 123 = 333 (no borrowing needed)

Single borrowing: 324 - 157 = 167 (borrow from tens)

Double borrowing: 502 - 187 = 315 (borrow from hundreds then tens)

With zeros: 600 - 234 = 366 (multiple borrowing needed)

Tips and Tricks:

• Use base ten blocks or visual aids to understand borrowing

• Always check your work by adding the difference to the subtrahend

• When borrowing: decrease the higher place by 1 and increase the lower place by 10

• Practice with small numbers first, then progress to larger numbers

Common Pitfalls:

• Forgetting to adjust the higher place after borrowing

• Subtracting the smaller number from the larger regardless of position

• Misaligning digits when writing numbers vertically

• Not carrying over borrowed amounts properly

Key Notes for Memorization:

• Memory aid: "More on top, don't stop. More on bottom, borrow from the next door"

• Verification trick: Always add your answer to the number you subtracted to check if you get the original number

• Direction rule: Right to left, just like reading but backwards

• Place value importance: Each position is 10 times the position to its right

• Borrowing effect: When you borrow, you're really taking 10 from the higher place to add to the lower place

Questions & Answers

Question: My child is confused about when to borrow in subtraction. How can I explain this clearly?

Answer: Explain borrowing with a simple rule: "When the top number is smaller than the bottom number in any column, you need to borrow from the next column to the left."

Use this memory aid: "More on top, don't stop. More on bottom, borrow from the next door!"

For example, in 32 - 17, when looking at ones place (2 and 7), since 2 is less than 7, you need to borrow from the tens place. Take 1 ten (which is 10 ones) and add it to the 2 ones, making it 12 ones. Then subtract: 12 - 7 = 5.

Question: Why do we sometimes need to borrow twice in one subtraction problem?

Answer: You need to borrow twice when both the tens and ones places have smaller top numbers than bottom numbers.

For example, in 402 - 187:

  • Look at ones: 2 < 7, so need to borrow from tens
  • But tens shows 0, and 0 < 8, so first borrow from hundreds
  • 4 hundreds becomes 3 hundreds, 0 tens becomes 10 tens
  • Now borrow from tens: 10 tens becomes 9 tens, 2 ones becomes 12 ones
  • Now you can subtract: 12-7=5, 9-8=1, 3-1=2

So 402 - 187 = 215.

Question: What are effective strategies to help students who struggle with place value subtraction?

Answer: Try these strategies:

  • Concrete materials: Use base ten blocks to physically show borrowing and regrouping
  • Visual aids: Draw place value charts and show exchanges clearly
  • Step-by-step instructions: Break the process into clear, manageable steps
  • Verification: Teach students to always check by adding the difference to the subtrahend
  • Pattern practice: Start with simple problems and gradually increase complexity

Also emphasize the relationship between addition and subtraction as inverse operations.